Surface source models and formulas for the magnetic field of polygonal cross section conductors

The magnetic field of long, straight conductors of arbitrary polygonal cross section, carrying current of given volume density, is modeled in terms of a distribution of fictitious magnetization inside each conductor and a distribution of fictitious surface current, using the Amperian model for magnetized media. Subsequently, this magnetization is replaced by an equivalent distribution of fictitious magnetic surface charge. As a result, the field calculation is reduced to that of the field due to a long strip of finite width, with simple distributions of surface charge and current. An elementary formula is derived for the field produced by a conductor of arbitrary polygonal cross section carrying a uniformly distributed current. The amount of computation is subsequently reduced compared to that needed for other methods, since a Laplacian scalar potential can be used in the absence of volume current density in these models